Problem: Simplify the following expression: $x = \dfrac{n^2 + 6n - 7}{n + 7} $
Explanation: First factor the polynomial in the numerator. $ n^2 + 6n - 7 = (n + 7)(n - 1) $ So we can rewrite the expression as: $x = \dfrac{(n + 7)(n - 1)}{n + 7} $ We can divide the numerator and denominator by $(n + 7)$ on condition that $n \neq -7$ Therefore $x = n - 1; n \neq -7$